Starting from Kepler's laws of planetary motion, this paper applies the real-particle theory to study the motion property and quantum behavior of the solar system. The solar system is a typical multi-body cluster (real particle) that has three motion modes of translation, rotation, and vibration. In a two-dimensional case, the earth/solar system is a two-body cluster that moves in its orbital plane and can be modeled as a rotating vibrator. The classical state function of the vibrator is an elliptic equation, and the quantum state function is a mapping of the elliptic equation to the complex plane. The state function contains the information of the cluster motion and satisfy the Schrödinger equation. The study shows that the quantum state function characterizes a time-averaged property of cluster motion, and the Schrödinger equation is a mapping algorithm from the potential function to the state function. The parameters of a planetary orbit are implicit variables of the quantum state, and the statistics of cluster motion are the reality basis of quantum mechanics.